What is the density (in $g m / l i t$ ) of wet air with $75 %$ relative humidity at $1 a t m$ and $300 K$ ? Given : vapour pressure of $H_{2} O$ is $30 t o r r$ and average molar mass of air is $29 g / m o l$ .
Write as the nearest integer:

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Solution

$%$ Relative humidity $= \frac{P a r t i a l p r e s s u r e o f H_{2} O}{V a p o u r p r e s s u r e o f H_{2} O} \times 100$
$75 = \frac{P_{H_{2} O}}{30} \times 100$
$P_{H_{2} O} = 22.5 t o r r$
$% o f H_{2} O$ vapour in air $= \frac{(22.5)}{760} \times 100 = 2.96$
molar mass of wet air $= \frac{29 \times 97.04 + 2.96 \times 18}{100}$
$= \frac{2814.16 + 53.28}{100} = 28.67$
density of wet air $= \frac{P M}{R T} = \frac{1 \times 28.67}{0.0821 \times 300}$
$= 1.164 g / L$
so nearest integer value is 1.

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